Pith Number

pith:CID2OUK4

pith:2021:CID2OUK4FICGXVJYQUFDAVLBKV

not attested not anchored not stored refs pending

Categorical Torelli theorems for Gushel-Mukai threefolds

Augustinas Jacovskis, Shizhuo Zhang, Xun Lin, Zhiyu Liu

arxiv:2108.02946 v4 · 2021-08-06 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CID2OUK4FICGXVJYQUFDAVLBKV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T07:48:26.347939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1207a7515c2a046bd538850a305561555d6a67348a1b9062a61ba8d24a4e27a5

Aliases

arxiv: 2108.02946 · arxiv_version: 2108.02946v4 · doi: 10.48550/arxiv.2108.02946 · pith_short_12: CID2OUK4FICG · pith_short_16: CID2OUK4FICGXVJY · pith_short_8: CID2OUK4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CID2OUK4FICGXVJYQUFDAVLBKV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1207a7515c2a046bd538850a305561555d6a67348a1b9062a61ba8d24a4e27a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85e39c6986bfe6fe44b1817d06a15cba2374dc4b582d95dba40c600bff064dc5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-08-06T05:45:39Z",
    "title_canon_sha256": "39ddb7bd078a67a91518f043d989305b3a45ee46d999fee0836cd28e5c17815a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.02946",
    "kind": "arxiv",
    "version": 4
  }
}